Evaluate The Expression: $\[(\sqrt{9})^2 + 5 = ?\\]

Introduction

In mathematics, expressions are a combination of numbers, variables, and mathematical operations that can be evaluated to produce a result. Evaluating an expression involves following the order of operations (PEMDAS) and simplifying the expression to obtain a final value. In this article, we will evaluate the expression $(\sqrt{9})^2 + 5$ and explore the concepts of square roots and exponents.

Understanding Square Roots

A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4, because $4 \times 4 = 16$. The square root of a number is denoted by the symbol $\sqrt{}$. In the given expression, we have $\sqrt{9}$, which means we need to find the value of $x$ such that $x \times x = 9$.

Evaluating the Square Root

To evaluate the square root of 9, we need to find the value of $x$ such that $x \times x = 9$. We know that $3 \times 3 = 9$, so the square root of 9 is 3. Therefore, $\sqrt{9} = 3$.

Understanding Exponents

An exponent is a small number that is raised to a power, indicating how many times the base number should be multiplied by itself. For example, $2^3$ means 2 multiplied by itself 3 times, which is equal to $2 \times 2 \times 2 = 8$. In the given expression, we have $(\sqrt{9})^2$, which means we need to raise the value of $\sqrt{9}$ to the power of 2.

Evaluating the Exponent

To evaluate the exponent $(\sqrt{9})^2$, we need to raise the value of $\sqrt{9}$ to the power of 2. We already know that $\sqrt{9} = 3$, so $(\sqrt{9})^2 = 3^2$. To evaluate $3^2$, we need to multiply 3 by itself 2 times, which is equal to $3 \times 3 = 9$.

Adding 5 to the Result

Now that we have evaluated the exponent $(\sqrt{9})^2$, we need to add 5 to the result. We already know that $(\sqrt{9})^2 = 9$, so adding 5 to the result gives us $9 + 5 = 14$.

Conclusion

In conclusion, evaluating the expression $(\sqrt{9})^2 + 5$ involves understanding the concepts of square roots and exponents. We found that $\sqrt{9} = 3$, and then raised 3 to the power of 2 to get 9. Finally, we added 5 to the result to get 14. Therefore, the final answer to the expression is 14.

Frequently Asked Questions

• What is the square root of 9? The square root of 9 is 3.
• What is the value of $(\sqrt{9})^2$? The value of $(\sqrt{9})^2$ is 9.
• What is the final answer to the expression $(\sqrt{9})^2 + 5$? The final answer to the expression $(\sqrt{9})^2 + 5$ is 14.

Final Answer

The final answer to the expression $(\sqrt{9})^2 + 5$ is $\boxed{14}$.

Introduction

In our previous article, we evaluated the expression $(\sqrt{9})^2 + 5$ and explored the concepts of square roots and exponents. In this article, we will answer some frequently asked questions related to evaluating expressions with square roots and exponents.

Q&A

Q: What is the square root of 16?

A: The square root of 16 is 4, because $4 \times 4 = 16$.

Q: What is the value of $(\sqrt{25})^2$?

A: The value of $(\sqrt{25})^2$ is 25, because $\sqrt{25} = 5$ and $5^2 = 25$.

Q: What is the final answer to the expression $(\sqrt{36})^2 + 3$?

A: The final answer to the expression $(\sqrt{36})^2 + 3$ is 39. We know that $\sqrt{36} = 6$, so $(\sqrt{36})^2 = 6^2 = 36$. Adding 3 to the result gives us $36 + 3 = 39$.

Q: What is the value of $(\sqrt{49})^3$?

A: The value of $(\sqrt{49})^3$ is 343. We know that $\sqrt{49} = 7$, so $(\sqrt{49})^3 = 7^3 = 7 \times 7 \times 7 = 343$.

Q: What is the final answer to the expression $(\sqrt{81})^2 + 2$?

A: The final answer to the expression $(\sqrt{81})^2 + 2$ is 83. We know that $\sqrt{81} = 9$, so $(\sqrt{81})^2 = 9^2 = 81$. Adding 2 to the result gives us $81 + 2 = 83$.

Q: What is the value of $(\sqrt{4})^4$?

A: The value of $(\sqrt{4})^4$ is 16. We know that $\sqrt{4} = 2$, so $(\sqrt{4})^4 = 2^4 = 2 \times 2 \times 2 \times 2 = 16$.

Conclusion

In conclusion, evaluating expressions with square roots and exponents requires a good understanding of the concepts of square roots and exponents. By following the order of operations and simplifying the expression, we can arrive at the final answer. We hope that this Q&A article has helped to clarify any doubts you may have had about evaluating expressions with square roots and exponents.

Frequently Asked Questions

• What is the square root of 25? The square root of 25 is 5.
• What is the value of $(\sqrt{49})^2$? The value of $(\sqrt{49})^2$ is 49.
• What is the final answer to the expression $(\sqrt{36})^2 + 2$? The final answer to the expression $(\sqrt{36})^2 + 2$ is 38.

Final Answer

The final answer to the expression $(\sqrt{9})^2 + 5$ is $\boxed{14}$.